In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places. 𝜋/13 radians

Verified step by step guidance

1. Recall the formula to convert radians to degrees: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).
2. Substitute the given angle \(\frac{\pi}{13}\) radians into the formula: \(\text{degrees} = \frac{\pi}{13} \times \frac{180}{\pi}\).
3. Simplify the expression by canceling out \(\pi\): \(\text{degrees} = \frac{180}{13}\).
4. Divide 180 by 13 to get the decimal value of the angle in degrees.
5. Round the result to two decimal places as required.

Key Concepts

Radian Measure

A radian is a unit of angular measure based on the radius of a circle. One radian is the angle created when the arc length equals the radius. It is a standard unit in trigonometry and is related to degrees by the formula 2π radians = 360 degrees.

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian measure by 180/π. This conversion factor comes from the equivalence of 2π radians to 360 degrees, simplifying to 1 radian = 180/π degrees.

Rounding Decimal Values

After converting the angle to degrees, round the result to the specified number of decimal places, in this case, two. Rounding ensures the answer is precise and presented in a standard format for clarity.